Summary: This paper provides a simple numerical method for checking the normality of estimators such as the least squares estimator and the maximum likelihood estimator. Instead of conventional analysis in which the parameter of interest is fixed, we allow the parameter to move in some parameter space. For each parameter sampled randomly out of the space, we get the parameter estimate and construct the Wald type test statistic which is used for checking normality of the estimator.
We carry out several numerical experiments in a linear regression model and time series models such as AR, ARCH, GARCH and EGARCH to see how the estimators behave as the sample sizes are increasing. The results imply that conditional heteroscedasticity models require relatively large samples for good approximation of normality.